By means of supersymmetric quantum mechanics, we provide a new simple proof that discrete eigenstates, i.e., bound states, of any one‐dimensional quantum system satisfying the time‐independent Schrödinger equation without internal degrees of freedom are nondegenerate. Using the same idea, we show that the ground state of anN‐dimensional time‐independent Schrödinger equation without internal degrees of freedom is nondegenerate, too. Reasons why degeneracy is possible for excited states whenN≳1 are also discussed.